As the use of ultrafast pulses has become more widespread in research and applications, the requirements and standards for control and characterization of the pulse and beam quality have become more stringent. Characterization of the temporal structure of pulses is well-developed with techniques such as frequency-resolved optical gating (FROG) and spectral phase interferometry for direct electric-field reconstruction (SPIDER). These techniques and their variants are typically used to characterize the amplitude and phase of pulses that have a pulse shape that does not depend on position within the beam. However, spatio-temporally coupled pulses cannot be written in a separable product form, such as E(r,t)=f(r)g(t). Generally, in this case, there is an arbitrary variation in the pulse's structure with respect to position in the beam, which may result from a complicated nonlinear interaction such as filamentation.
In many cases, spatial chirp is an undesired (and often unrecognized) result of a misalignment in a chirped-pulse amplifier (CPA) system. An extension of the compressor alignment issue is grating tiling where multiple gratings are used in high-energy lasers instead of a large single grating. Angularly chirped beams can arise directly as the idler in non-collinear optical parametric amplifiers. Over the years, experiments have shown that spatial chirp and pulse front tilt can be exploited: traveling-wave pumping of X-ray lasers and pulse front matching in nonlinear optics and terahertz generation. More recently, systems have been developed to explicitly take advantage of the geometric second-order phase that results from angular chirp for temporal focusing. Accordingly, an increasing interest in exploiting the spatio-temporal qualities of these beams exists. Temporal focusing leads to axial sectioning in wide-field microscopy; simultaneous spatial and temporal focusing (SSTF) results in intensity localization useful in micro-machining and laser surgery. The pulse front tilt (PFT) that results from angular spatial chirp offers a means to control nonlinear conversion and is important in the phenomenon of nonreciprocal writing. Also, generation of attosecond pulses spatially separated in the far field can be obtained from the lighthouse effect, which utilizes rotation of the wavefront resulting from lateral chirp at the target. In these applications, understanding and controlling the nonlinear dynamics requires knowledge of the spatio-temporal characteristics of these ultrafast pulses.
Although general spatio-temporal characterization methods exist, such methods generally need a reference beam that is free of spatio-temporal distortion as well as the characterization of the input beam. Also, in such methods as STRIPED FISH, the spatial and spectral resolutions are limited by optics in the hologram design. Accordingly, improved characterization and control over a beam's spatio-temporal characteristics are needed in CPA and SSTF compressor systems.